Motivated by the potential of nondiffraction limited, real-time computational image sharpening with neural networks in astronomical telescopes, we studied wavefront sensing with convolutional neural networks based on a pair of in-focus and out-of-focus point spread functions. By simulation, we generated a large dataset for training and validation of neural networks and trained several networks to estimate Zernike polynomial approximations for the incoming wavefront. We included the effect of noise, guide star magnitude, blurring by wide-band imaging, and bit depth. We conclude that the "ResNet" works well for our purpose, with a wavefront RMS error of 130 nm for r 0 ¼ 0.3 m, guide star magnitudes 4 to 8, and inference time of 8 ms. It can also be applied for closed-loop operation in an adaptive optics system. We also studied the possible use of a Kalman filter or a recurrent neural network and found that they were not beneficial to the performance of our wavefront sensor. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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The Euro50 is an astronomical extremely large telescope for optical and infrared wavelength with a 50 m primary mirror. The telescope will have an elaborate control system ("live optics") to correct for atmospheric and telescope aberrations. To study and predict performance of the complete telescope system, an integrated model combining the structural model of the telescope, optics models, the control systems, and the adaptive optics has been established. Wind is taken into account on the basis of wind tunnel measurements and computer fluid dynamics calculations. Atmospheric aberrations are included using a seven-layer atmosphere model. The integrated model is written in Matlab and is run on a cluster computer to achieve acceptable execution times. Dedicated ordinary differential equation solvers have been written and a special toolkit for communication between Matlab processes on different nodes of the cluster computer has been set up. Preliminary results from the complete integrated model, including adaptive optics, are shown.

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